diff --git a/src/1_complex_numbers.md b/src/1_complex_numbers.md index 20b6f3dab5fdd80670a9d90ef8e05bf7910e5956..fcc89d84ebb7db58b7bea1f2e58931b17e1dce14 100644 --- a/src/1_complex_numbers.md +++ b/src/1_complex_numbers.md @@ -159,6 +159,9 @@ $$z^{n} = \left(r e^{{\rm i} \varphi}\right)^{n} = r^{n} e^{{\rm i} n \varphi}$$ $$\sqrt[n]{z} = \sqrt[n]{r e^{{\rm i} \varphi} } = \sqrt[n]{r} e^{{\rm i}\varphi/n} $$ $$\log(z) = log \left(r e^{{\rm i} \varphi}\right) = log(r) + {\rm i} \varphi$$ $$z_{1}z_{2} = r_{1} e^{{\rm i} \varphi_{1}} r_{2} e^{{\rm i} \varphi_{2}} = r_{1} r_{2} e^{{\rm i} (\varphi_{1} + \varphi_{2}}$$ +We see that during multiplication, the norm of the new number is the *product* of the norms of the multiplied numbers, and its argument is the *sum* of the arguments of the multiplied numbers. In the complex plane, this looks as follows: + + ### Differentiation and integration We only consider differentiation and integration over *real* variables. 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